Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D92×C3⋊D3 |
| Fitting, derived, Sylow | C32×C92 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C92 | C23 |
| Frattini | C32 | D32×C3⋊D3 |
| socle | C34 | C2×D32 |
| LCS | G ▷ C32×C92 | |
| UCS | C1 | |
1922 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 1922 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#92265⋊C2, D32×D92, D9×D9⋊((C3⋊D3)⋊C3), … |
| maximal normal subgroup of | C3⋊D3×#92265⋊C2, D32×D92, D9×D9⋊((C3⋊D3)⋊C3), … |
Past the SmallGroups library coverage — no SmallGroups id.